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Sat, 11 Oct 2003 10:38:04 +0100Sat, 11 Oct 2003 10:38:04 +0100On the adaptive selection of the parameter in regularization of ill-posed problemshttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1445
We study a possiblity to use the structure of the regularization error for a posteriori choice of the regularization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko (1964), and to an adaptation scheme proposed in a statistical context by Lepskii (1990), is discussed. The advantages of the proposed criterion are illustrated by using such examples as self-regularization of the trapezoidal rule for noisy Abel-type integral equations, Lavrentiev regularization for non-linear ill-posed problems and an inverse problem of the two-dimensional profile reconstruction.Sergei Pereverzev; Eberhard Schockpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1445Mon, 10 Nov 2003 10:38:04 +0100